A nonrelativistic quantum field theory with point interactions in three dimensions

Abstract

We construct a Hamiltonian for a quantum-mechanical model of nonrelativistic particles in three dimensions interacting via the creation and annihilation of a second type of nonrelativistic particles, which are bosons. The interaction between the two types of particles is a point interaction concentrated on the points in configuration space where the positions of two different particles coincide. We define the operator, and its domain of self-adjointness, in terms of co-dimension-three boundary conditions on the set of collision configurations relating sectors with different numbers of particles.

arXiv commentv4: Additional references

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Cited by in corpus (15)

• Hamiltonians Without Ultraviolet Divergence for Quantum Field Theories
• On Bohmian Mechanics, Particle Creation, and Relativistic Space-Time: Happy 100th Birthday, David Bohm!
• The Renormalised Bogoliubov-Fröhlich Hamiltonian
• On a Direct Description of Pseudorelativistic Nelson Hamiltonians
• On the self-adjointness of H+A*+A
• The resolvent of the Nelson Hamiltonian improves positivity
• Hamiltonians for polaron models with subcritical ultraviolet singularities
• Interior-Boundary Conditions for Schrodinger Operators on Codimension-1 Boundaries
• Interior-Boundary Conditions for the Dirac Equation at Point Sources in 3 Dimensions
• Extended State Space for describing renormalized Fock spaces in QFT
• Boundary Conditions that Remove Certain Ultraviolet Divergences
• A Lower Bound on the Critical Momentum of an Impurity in a Bose-Einstein Condensate
• The excitation spectrum of a Bose gas with an impurity in the Gross-Pitaevskii regime
• Self-adjointness and domain of generalized spin-boson models with mild ultraviolet divergences
• Implementing Bogoliubov Transformations Beyond the Shale-Stinespring Condition